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组间方差和自相关系数的齐性是纵向数据分析的基本假设之一,然而这种假设需要进行统计检验. Zhang \&; Weiss$^{[15]}$ 讨论了线性随机效应模型的组间和组内方差齐性的检验问题;林金官 \&; 韦博成$^{[10]}$ 研究了具有AR(1)误差但没有随机效应的非线性模型的自相关系数的齐性检验.该文研究具有随机效应和AR(1)误差的非线性模型的组间方差和自相关系数的齐性检验问题,构造了几个score检验统计量, 并通过Monte Carlo模拟方法研究了检验统计量的性质.最后利用该文的方法分析一组实际数据和一组模拟数据. 相似文献
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方差和相关系数的齐性是纵向数据分析中常用假设之一,然而,这些假设未必合适.本文主要研究的是具有指数相关结构的纵向数据非线性混合效应模型,首先将Huber函数引入模型的对数似然函数中,利用Fisher得分迭代法得到模型参数的稳健估计(M估计),然后基于M估计对模型的方差和相关系数的齐性进行了Score检验,并给出了检验统计量的Monte-Carlo模拟结果.最后用一个实例说明了本文的方法. 相似文献
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非线性Poisson-Gamma回归模型中存在偏大离差时离差参数的齐性检验 总被引:1,自引:0,他引:1
Poisson回归模型广泛地应用于分析计数型数据,但该模型往往存在偏大离差(overdispersion)问题.刻画Poisson回归模型的偏大离差性的两种方法是拟似然方法和随机效应法(Lee&Nelder,2000),已有许多作者利用随机效应法研究了Poisson模型的偏大离差的检验问题.但他们均假定随机效应是独立同分布的,本文对他们的假设进行检验.我们分别在组内效应一致和组内效应不一致的情形下,研究了存在偏大离差的Poisson-Gamma非线性随机效应模型中,随机效应方差(称为离差参数)的齐性检验问题,得到了离差参数齐性的score检验统计量.最后给出两个数值例子说明本文方法的应用. 相似文献
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非线性随机效应模型的异方差性检验 总被引:11,自引:0,他引:11
随机效应模型广泛应用于刻画重复测量数据的特征.在该模型中,随机误差的方差包括受试群体内部及受试群体之间两项方差.Zhang和 Weiss 2000年研究了线性随机效应模型的异方差检验,本文对非线性随机效应模型,分别讨论了群体内、群体间和多变量的异方差性的检验问题,得到了检验的score统计量,并讨论了三种情形下,相应的score函数之间的关系.最后给出一个数值例子说明上述方法的有用性. 相似文献
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在回归分析中,随机误差是否存在方差齐性是理论与实际工作者都十分关心的问题,方差齐性假设并不总是正确的,在线性和非线性回归中关于异方差的诊断问题已有许多讨论([1],[2],[4],[5])。本文在韦博成(1995)讨论了加权非线性回归模型的基础上,用随机系数的方法,讨论随机权函数非线性回归模型中的异方差检验问题,得到了方差齐性检验的似然比统计量和score统计量,同时,当模型存在异方差时,本文给出了估计方差的一种方法。 相似文献
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非线性纵向数据模型中自相关性和随机效应的存在性检验 总被引:2,自引:2,他引:0
刻画纵向数据协方差结构有三种可能因素 ,即序列相关 (特别是一阶自相关 )、随机效应和常规的随机误差 (Diggleetal,2 0 0 2 ) .本文研究非线性纵向数据模型的自相关性和随机效应存在性的单个和联合检验 ,得到了检验的score统计量 ,并利用血浆药物渗透数据 (Davidian&Gilinan ,1 995)说明检验方法的应用 . 相似文献
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Homogeneity of variance and correlation coefficients is one of assumptions in the analysis of longitudinal data.However, the assumption can be challenged. In this paper, we mainly propose and analyze nonlinear mixed effects models for longitudinal data with exponential correlation covariance structure, intend to introduce Huber's function in the log likelihood function and get robust estimation (M-estimation) by Fisher scoring method. Score test statistics for homogeneity of variance and correlation coefficient based on M-estimation are then studied. A simulation study is carried to assess the performance of test statistics and the method we proposed in the paper is illustrated by an actual data example. 相似文献
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在时间序列回归模型分析中,相关性和方差齐性的检验是一个很基本的问题.本文讨论了具有双线性BL(1,1,1,1)误差的非线性回归模型的相关性和方差齐性的检验问题, 用Score检验方法给出了双线性项检验、相关性检验、方差齐性检验、以及相关性和方差齐性同时检验的检验统计量.推广和发展了具有线性序列误差项回归模型的结果.本文还用数值实例说明了检验方法的实用价值. 相似文献
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Y. Boubacar Mainassara 《Journal of multivariate analysis》2011,102(3):496-505
The asymptotic properties of the quasi-maximum likelihood estimator (QMLE) of vector autoregressive moving-average (VARMA) models are derived under the assumption that the errors are uncorrelated but not necessarily independent nor martingale differences. Relaxing the martingale difference assumption on the errors considerably extends the range of application of the VARMA models, and allows one to cover linear representations of general nonlinear processes. Conditions are given for the asymptotic normality of the QMLE. Particular attention is given to the estimation of the asymptotic variance matrix, which may be very different from that obtained in the standard framework. 相似文献
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Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity (Kantz and Schreiber (1997)). Tsai (1986) introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR(1) errors. Liu (2003) introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL(p, 0, 1) errors. Therefore, the important problems in regres- sion model are detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL(p, q, 1) random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedas-ticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai (1986), Wei, et al (1995), and Liu, et al (2003). 相似文献
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A general Bayesian approach for stochastic versions of deterministic growth models is presented to provide predictions for crack propagation in an early stage of the growth process. To improve the prediction, the information of other crack growth processes is used in a hierarchical (mixed‐effects) model. Two stochastic versions of a deterministic growth model are compared. One is a nonlinear regression setup where the trajectory is assumed to be the solution of an ordinary differential equation with additive errors. The other is a diffusion model defined by a stochastic differential equation where increments have additive errors. While Bayesian prediction is known for hierarchical models based on nonlinear regression, we propose a new Bayesian prediction method for hierarchical diffusion models. Six growth models for each of the two approaches are compared with respect to their ability to predict the crack propagation in a large data example. Surprisingly, the stochastic differential equation approach has no advantage concerning the prediction compared with the nonlinear regression setup, although the diffusion model seems more appropriate for crack growth. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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H. T. Abebe F. E. S. Tan G. J. P. Van Breukelen M. P. F. Berger 《Computational Statistics》2014,29(6):1667-1690
In medicine and health sciences mixed effects models are often used to study time-structured data. Optimal designs for such studies have been shown useful to improve the precision of the estimators of the parameters. However, optimal designs for such studies are often derived under the assumption of a zero autocorrelation between the errors, especially for binary data. Ignoring or misspecifying the autocorrelation in the design stage can result in loss of efficiency. This paper addresses robustness of Bayesian D-optimal designs for the logistic mixed effects model for longitudinal data with a linear or quadratic time effect against incorrect specification of the autocorrelation. To find the Bayesian D-optimal allocations of time points for different values of the autocorrelation, under different priors for the fixed effects and different covariance structures of the random effects, a scalar function of the approximate variance–covariance matrix of the fixed effects is optimized. Two approximations are compared; one based on a first order penalized quasi likelihood (PQL1) and one based on an extended version of the generalized estimating equations (GEE). The results show that Bayesian D-optimal allocations of time points are robust against misspecification of the autocorrelation and are approximately equally spaced. Moreover, PQL1 and extended GEE give essentially the same Bayesian D-optimal allocation of time points for a given subject-to-measurement cost ratio. Furthermore, Bayesian optimal designs are hardly affected either by the choice of a covariance structure or by the choice of a prior distribution. 相似文献
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TESTING FOR VARYING DISPERSION OF LONGITUDINAL BINOMIAL DATA IN NONLINEAR LOGISTIC MODELS WITH RANDOM EFFECTS 总被引:1,自引:0,他引:1
In this paper, it is discussed that two tests for varying dispersion of binomial data in the framework of nonlinear logistic models with random effects, which are widely used in analyzing longitudinal binomial data. One is the individual test and power calculation for varying dispersion through testing the randomness of cluster effects, which is extensions of Dean(1992) and Commenges et al (1994). The second test is the composite test for varying dispersion through simultaneously testing the randomness of cluster effects and the equality of random-effect means. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas. The authors illustrate their test methods using the insecticide data (Giltinan, Capizzi & Malani (1988)). 相似文献